Channel-facilitated membrane transport. (i) We developed a general theory of fluctuations of ion current through a membrane channel due to partial blocking of the channel by translocating molecules. (ii) We developed a theory of transport of molecules through conical channels and showed that inter-particle interactions break the flux symmetry inherent in transport of non-interacting particles through such channels. Two-state protein folding. We developed a theory of two-state protein folding assuming that underlying dynamics is formulated in terms of rate equations on a network of coarse-grained discrete states of the protein. Our theory allows one to find folding and unfolding rates as well as most probable folding/unfolding pathways. Dynamics of morphogen gradients in the Drosophila Embrio. We developed a theory of signaling gradients in cascades of two-state reaction-diffusion systems that provides a new insight into the experimental observations made in Professor Shvartsman's Lab. at Princeton University. Transport in complex media with entropy traps and barriers. We developed a theory that explains anomalous dependence of the particle diffusivity on its radius for diffusion in tubes with dead ends. Diffusive escape from dendritic spines. We developed a theory that explains how the particle lifetime in a dendritic spine depends on geometric parameters of the spine, initial position of the particle, and its diffusivity in the spine neck and head.